256 
IONISATION, DIFFUSION, ROTATION 
We conclude that the effect on the brightness of the stars of the 
difference of molecular weight arising from differences of internal condition 
is inconsiderable, amounting at the outside to or ^ of a magnitude*. 
We can also find from Table 32 the effect of an error of 0-1 in the 
adopted average molecular weight for all stars. Since the comparisons are 
differential with respect to Capella we have in that case to subtract 0 m T6 
from the column — Am. 
179. The reduction of opacity caused by the “guillotine” (according 
to Kramers’ theory) depends on < h/RT; the corresponding reduction 
factors have been found in § 160. For Capella ifjJRT = 8 and there is no 
appreciable effect. But for the sun ifjJBT = 4 and the opacity is reduced 
in the ratio 4-5; this would make it l m -6 brighter. The guillotine correction 
would accordingly upset the good accordance between theory and observa 
tion. For Krueger 60 the brightness would be increased by 4 or 5 mag 
nitudes; it is true that this star is somewhat brighter than the original 
prediction, but this may be accounted for in another way and the guillotine 
correction is much too large. 
If the guillotine correction had been applied in Fig. 2 the accordance 
of theory and observation would have been far from satisfactory. 
The values of tfj^RT in Tables 31 a and 31 b have been calculated in 
a very provisional way and it may perhaps be suggested that more 
accurate computation would remove this difficulty. I do not think this 
is so; the more obvious corrections needed for a second approximation 
tend to reduce the values of i/jJRT. 
This seems to affect very seriously the position of Kramers’ theory of 
absorption as applied to the stars. An absorption law approximating to 
p/T 7 - is suggested (as we have seen) by extremely general considerations, 
and the fact that the stars seem to obey it cannot be regarded as favouring 
Kramers’ -theory in particular. When we turn to the features more especially 
characteristic of his theory we meet with failure; the absolute constant 
in the formula is considerably too small, and the peculiar modification 
caused by the cutting off of high frequency radiation seems to be decisively 
contradicted. 
180. The foregoing discussion aimed at a general survey of the problem 
without attempting high accuracy. It may be supplemented by the 
numerical results of Fowler and Guggenheim f who have made extensive 
calculations for typical stars and typical elements taking into account 
many refinements of the theory of ionisation. 
* Some reservation should be made in the case of stars of mass less than half 
that of the sun owing to the low value of ifj-y/RT. 
f Monthly Notices, 85, p. 939 (1925).